American manufacturing hit an important milestone in April, when the Commerce Department reported that the sector had recovered all the value lost in the recession.

That sort of good news may be difficult to see in places like Danville, Ill., which has been hard-hit by factory closings. One out of every 5 jobs in Danville is in manufacturing, and those jobs are rapidly disappearing. The city of 33,000 lost about 1,600 manufacturing jobs during the recession. Now, the town’s economic development agency touts the growth of its retail sector.

Danville’s experience indicates that the story of manufacturing’s comeback is more complicated than the broad-brush numbers. Scratch below the surface of the data from Commerce Department’s Bureau of Economic Analysis and it’s hard to declare the industry fully healed.

For instance, how can the manufacturing sector’s value-added measure post such impressive gains when the gap between U.S. exports and imports remains so wide? Even as plants produce more, why has manufacturing only added back a quarter of the 2.3 million jobs lost in the recession? And why is the pace of job growth slowing down — manufacturers added 178,000 jobs in 2011, but only 128,000 in 2012 and 71,000 in 2013 — even though manufacturing’s contributions to the economy are picking up?

For policymakers, getting a clear picture of American manufacturing is important as Washington looks to boost a steady but sluggish recovery and expand hiring. Bolstering manufacturing makes sense if the sector is on the upswing. But lawmakers might hesitate to throw money at an industry that has dim long-term prospects.

Misleading Scenarios

According to many economists, unreliable government data is leading to overly rosy conclusions about the health of the manufacturing industry. Imports are not properly measured, for instance. And the rapid changes in the computer industry tends to skew the numbers.

“You think your manufacturing is growing, but it may be shrinking, and you don’t know the right places to apply policy levers,” said Michael Mandel, an economist at the Progressive Policy Institute who has spent years studying these issues. “At this point, in manufacturing we’re flying blind.”

Manufacturing may be making a comeback, but that rebound could be far more modest and shorter-lived than initial numbers would suggest. As a warning, the Bureau of Labor Statistics predicts that manufacturing will lose more than half a million jobs between 2012 and 2022.

“The manufacturing sector is really weaker than it appears in the data,” said Susan Houseman, an economist at the W.E. Upjohn Institute for Employment Research, a Michigan-based think tank.

This hasn’t stopped Washington from pouncing on the idea of a “manufacturing renaissance” driven by increased productivity in American factories.

In his 2014 State of the Union address, President Barack Obama hailed “a manufacturing sector that’s adding jobs for the first time since the 1990s.”

The administration has also launched two “innovation hubs,” in Youngstown, Ohio, and Raleigh, N.C., designed to bring research and development closer to production. The idea is that by linking the two, companies will be more inclined to keep production jobs in the United States. Two more hubs are planned for Detroit and Chicago.

On Capitol Hill, Democrats such as Rep. Robin Kelly of Illinois note the manufacturing rebound and argue for tax credits for employers who hire veterans or people on certain government assistance programs.

Republicans, on the other hand, say manufacturing’s recent successes point to the need for fewer government regulations and more domestic energy production.

Chad Moutray, chief economist at the National Association of Manufacturers, credits high-tech, super-productive factories making more valuable goods for the resurgence.

“Manufacturing has become more competitive on the global stage as manufacturing has become more lean,” he said.

In a recent series of bullish reports, the Boston Consulting Group argued that rising labor costs in China will also prompt firms to move production back to the United States. That will lead the United States to pick up between 2 million and 3 million jobs by the end of the decade, the firm says, contradicting the more somber projections from the BLS.

That’s quite a change from the 2000s, when a collapsing manufacturing industry, buffeted by Chinese competition, was almost given up for dead.

But some economists say the benefits of shifting global trends in costs and productivity, while real, have been inflated.

“The story you often hear — that output growth is healthy, that we’re seeing a lot of productivity growth so we’re not getting a lot of new jobs — is not quite right,” said Howard Wial, an economist at the University of Illinois at Chicago and a senior fellow at the Brookings Institution. “It’s become almost conventional wisdom. It’s, if not completely wrong, at least overstated.”

Shortcomings in Data

Many manufacturing experts say official statistics overstate manufacturing’s economic contributions because government statisticians do not have a good way to keep track of shifts to cheaper suppliers.

For instance, when an American manufacturer decides to switch from an American supplier to a cheaper foreign supplier, statisticians at the Commerce Department record that as a drop in inputs.

On paper, it seems as though the manufacturer is making more with less. In reality, that manufacturer still needs those supplies in the same quantity. It is simply paying less for them.

According to a 2011 paper by Houseman and three colleagues, this problem may have overstated the actual growth in manufacturing’s contributions to gross domestic product by about 20 percent between 1997 and 2007.

Houseman said a separate statistical quirk involving the computer and electronics industry also inflates manufacturing’s recent growth spurt. As computers have gotten both more powerful and cheaper, they have come to make up an outsized share of manufacturing’s contribution to the economy.

Today, consumers can buy much more computing power with their dollars than they could a few years ago. Government statisticians record that as an increase in the overall value that the computing industry adds to the economy. That’s why the computer and electronics industry’s contribution to overall economic growth surged more than sevenfold between 1997 and 2012, according to BEA data.

Remove the computer and electronics industry from the manufacturing equations, and you see the sector in a very different light. In fact, as Houseman noted, without computers and electronics, manufacturing has significantly underperformed the economy as a whole.

“It’s this big outlier that just jerks the numbers, and people should understand that,” Houseman said. “Everybody who talks about manufacturing policy should understand what the numbers are really saying.”

The complications and disputes over manufacturing data likely will only increase in the next few years, as statistical agencies move to a new way of counting manufacturing jobs at so-called factoryless goods producers.

Under the new measure, companies that keep some white-collar jobs in the United States but assemble their products in factories abroad could be counted as manufacturers.

That means that a designer at Apple could be counted as a manufacturing employee as long as Apple maintains ownership of its products when they’re shipped from a Chinese factory to the United States. That could produce a surge in the number of manufacturing jobs when the reclassification takes place in 2017.

“The whole definition of manufacturing is changing at this point,” Mandel said.

Government statisticians have been grappling with problems in the data for years. But better data collection is not cheap. And Congress is not likely to spend money on technical fixes in this era of austerity.

As a result, the country is likely to muddle along with misleading or inaccurate data. More troubling, Washington will continue to make policy without knowing what exactly it is up against.